a question of time, velocity and relativity

[CTRandall]

The simplest way I can put my question is like this: velocity is described as distance/time. That's a fine approximation at non-relativistic speeds. The closer an object gets to the speed of light, however, the more time slows for that object. So a distant observer would record one velocity for a near-light speed craft but, due to the slowing of time the passengers on the craft would record a much higher velocity.

Put another way, light travels as ca. 300,000 km/sec. But if I were to travel at close to the speed of light, from my perspective I would be travelling faster, as my seconds would be much slower than normal. It might appear to me that I was traversing 300,000 km in .5 sec, for example. I know physicists make a distinction between 'proper' time and 'coordinate' time. Measuring by proper time, i.e. the perspective of the traveller, seems to allow for perceived speeds greater than light. Is that right?

Also, is there an agreed perspective from which to establish 'coordinate' time? A kind of SI unit of velocity-observation? I suppose what I mean is, since time varies with velocity and everything is moving, what is the baseline from which we measure the velocity of objects. (And if you tell me it's the speed of light, I'm going to have a very big headache.)

Finally, is there a means of getting around this by measuring velocity independent of time?

 

[AllanR]

As you get to relativistic speeds, from your perspective, time slows but the distance decreases correspondingly.

from Length contraction - Wikipedia

where

• L is the length observed by an observer in motion relative to the object
• L0 is the proper length (the length of the object in its rest frame)
• γ(v) is the Lorentz factor, defined as
  
  
  
  
  where
  • v is the relative velocity between the observer and the moving object
  • c is the speed of light

 

[BAYLOR]

Time Dilation ?

 

[Venusian Broon]

The simplest way I can put my question is like this: velocity is described as distance/time. That's a fine approximation at non-relativistic speeds. The closer an object gets to the speed of light, however, the more time slows for that object.

Well, the closer a spacecraft gets to the speed of light, the more time slows relative to other (at rest) observers. However, those on the spacecraft would experience 'normal' time.

So a distant observer would record one velocity for a near-light speed craft but, due to the slowing of time the passengers on the craft would record a much higher velocity.

I am thinking late at night, and therefore may be very wrong...but yes there may well be a difference in observed velocities between observers in a 'rest' frame looking at a speeding spacecraft and those observers in the ship at a high speed. However both will be constrained by the fact that the speed of light is the same for all observers no matter what. And objects with mass cannot exceed the speed of light at all. (According to Relativity)

Put another way, light travels as ca. 300,000 km/sec. But if I were to travel at close to the speed of light, from my perspective I would be travelling faster, as my seconds would be much slower than normal.

No, your seconds, as you experience them, would be as normal as the ones that you experienced before you set out on you interstellar journey.

It might appear to me that I was traversing 300,000 km in .5 sec, for example.

No!

I know physicists make a distinction between 'proper' time and 'coordinate' time. Measuring by proper time, i.e. the perspective of the traveller, seems to allow for perceived speeds greater than light. Is that right?

No!! (I think....)

Also, is there an agreed perspective from which to establish 'coordinate' time? A kind of SI unit of velocity-observation? I suppose what I mean is, since time varies with velocity and everything is moving, what is the baseline from which we measure the velocity of objects. (And if you tell me it's the speed of light, I'm going to have a very big headache.)

No, everything is relative - according to Special Relativity - there is no objective 'baseline' that one can objectively measure every other frame. However, the speed of light is the same in all frames, no matter what you do. Hence the complicated mathematics.

Finally, is there a means of getting around this by measuring velocity independent of time?

Velocity by definition is: the rate at which position changes. I don't see how one could measure velocity without using 'time' differences

If the above makes no sense, give us more questions and criticism, I'm posting late and my thinking cap is fuzzy

 

[CTRandall]

@AllanR I don't think the length contraction of an object can be extrapolated to say that distance decreases. I'm not 100% sure of that but they seem to be two different beasts.

I am thinking late at night, and therefore may be very wrong...but yes there may well be a difference in observed velocities between observers in a 'rest' frame looking at a speeding spacecraft and those observers in the ship at a high speed.

This is really what I'm getting at, that there isn't a straightforward way of saying 'object x is moving at speed y'. Different observers are themselves moving at different velocities and different rates of time, so any measurement of velocity will always be relative to the observer. That's fine and dandy but...

there is no objective 'baseline' that one can objectively measure every other frame.

...in the absence of an agreed frame of reference, how is it possible to accurately communicate one's own observations to people who are experiencing a significantly different rate of time? If the answer is simply 'complicated mathematics', I have enough background in math that I can accept that. (Not that I'd have any hope of understanding the math, just that I can imagine some of the paths it might follow.)

Velocity by definition is: the rate at which position changes. I don't see how one could measure velocity without using 'time' differences

I know velocity is a pretty basic thing but it's funny how science occasionally has to rethink the basics, for example recognizing that matter can be converted to energy and vice versa. I was just checking if some clever clog had found a means of describing velocity in a different way--maybe by red-shift/blue-shift of light (though time is still an essential part of that--damn, for about 2 seconds I thought I was being clever ).

 

[Venusian Broon]

This is really what I'm getting at, that there isn't a straightforward way of saying 'object x is moving at speed y'. Different observers are themselves moving at different velocities and different rates of time, so any measurement of velocity will always be relative to the observer. That's fine and dandy but...


...in the absence of an agreed frame of reference, how is it possible to accurately communicate one's own observations to people who are experiencing a significantly different rate of time? If the answer is simply 'complicated mathematics', I have enough background in math that I can accept that. (Not that I'd have any hope of understanding the math, just that I can imagine some of the paths it might follow.)

Possibly the problem here is that we just don't experience noticeable different rates of time between two human observers. We just haven't been able to go fast enough for it to be recognisable - or at least fast relative to one another. A bit like Quantum mechanics and how the micro world is vastly different from the macro world - but we, hulking big macro beings can only see a 'classical' world, not a quantum one.

Now of course we have observed other things, such as gravitational lensing, Mercury's orbit, GPS, black holes etc... which suggests to us that Einstein's theories seem to be on point.

So if we could build an interstellar spacecraft that could attain 0.5 times the speed of light, we would be able to experience what it is like for two observers to communicate. Apart from the doppler shift, if two did communicate live, the person on the spacecraft would see a speed-up message from back on Earth, say. And what he speaks back would be slowed down for those listening back on Earth.

I know velocity is a pretty basic thing but it's funny how science occasionally has to rethink the basics, for example recognizing that matter can be converted to energy and vice versa. I was just checking if some clever clog had found a means of describing velocity in a different way--maybe by red-shift/blue-shift of light (though time is still an essential part of that--damn, for about 2 seconds I thought I was being clever ).

I'd have to give it a think.

But fundamentally time is weird and thinking about it usually gives rise to headaches

 

[BAYLOR]

Possibly the problem here is that we just don't experience noticeable different rates of time between two human observers. We just haven't been able to go fast enough for it to be recognisable - or at least fast relative to one another. A bit like Quantum mechanics and how the micro world is vastly different from the macro world - but we, hulking big macro beings can only see a 'classical' world, not a quantum one.

Now of course we have observed other things, such as gravitational lensing, Mercury's orbit, GPS, black holes etc... which suggests to us that Einstein's theories seem to be on point.

So if we could build an interstellar spacecraft that could attain 0.5 times the speed of light, we would be able to experience what it is like for two observers to communicate. Apart from the doppler shift, if two did communicate live, the person on the spacecraft would see a speed-up message from back on Earth, say. And what he speaks back would be slowed down for those listening back on Earth.





I'd have to give it a think.

But fundamentally time is weird and thinking about it usually gives rise to headaches

And object's mass become infinite as it approaches the Speed of light. This make it impossible for said best ever to each or exceed that speed. I cannot comprehend the mathematics involved here. It's beyond me.

 

[AllanR]

I don't think the length contraction of an object can be extrapolated to say that distance decreases. I'm not 100% sure of that but they seem to be two different beasts.

I thought that as well, but the answer to question 2 on page five being A, makes me think otherwise. https://physicsvce.weebly.com/uploads/1/2/4/9/124994336/length_contraction_solutions.pdf

 

[hitmouse]

I know velocity is a pretty basic thing but it's funny how science occasionally has to rethink the basics, for example recognizing that matter can be converted to energy and vice versa. I was just checking if some clever clog had found a means of describing velocity in a different way--maybe by red-shift/blue-shift of light (though time is still an essential part of that--damn, for about 2 seconds I thought I was being clever ).

Red-shift/Blue-shift really just describes light itself, which cannot travel at any speed other than C, so the wavelength changes depending on the velocity of the source compared to the observer.

 

[Wayne Mack]

I may be in over my head, but I suggest that distance dilation must occur to offset time dilation.

First, let me try to set up an example for the initial problem.

Suppose that there are two asteroids positioned one light-minute apart. A space ship flies past repeatedly at ever increasing speeds. An external observer will see the ship traverse the distance in ever decreasing times, approaching one minute.

An observer inside the ship would experience time dilation. Thus the internal observer will see the time to traverse the distance decrease at a faster rate than the external observer.

Given v = d/t, it would seem that the ship board observer would see the velocity to be greater than the external observer. Given we also know that v is bound, then the only way to offset the dilation in time is to also dilate distance observed within the moving ship.

The initial conundrum was generated by mixing frames of reference. It used the time period as observed ship board with the distance observed externally.

Just to be clear, the physics and mathematics behind this are outside my level of expertise. I have simply treated this as a logic problem nd the dilation of distance seems to be a logical conclusion to maintain the speed of light as a constant.

 

[CTRandall]

@AllanR The paper you linked to was worth it just for the drawing of the space ship and astronaut. Great to see a physics exam sprinkled with cartoons!

 

[CTRandall]

the wavelength changes depending on the velocity of the source compared to the observer.

Which was why I thought of it as an alternative means of describing velocity independent of time. I'm not sure we can distinguish wave-length from frequency (at least for this purpose) and frequency is a measured over time, which reintroduces the original problem.

 

[CTRandall]

I have simply treated this as a logic problem

I refer you back to Venusian Broon:

time is weird and thinking about it usually gives rise to headaches

 

[hitmouse]

Which was why I thought of it as an alternative means of describing velocity independent of time. I'm not sure we can distinguish wave-length from frequency (at least for this purpose) and frequency is a measured over time, which reintroduces the original problem.

Wavelength = velocity/frequency.

For light, velocity is a constant, C, and so wavelength and frequency are inextricably linked.

Since V = distance/time, which is fixed (C) for light, it is not possible to remove time from this relationship.

 

[Wayne Mack]

Which was why I thought of it as an alternative means of describing velocity independent of time. I'm not sure we can distinguish wave-length from frequency (at least for this purpose) and frequency is a measured over time, which reintroduces the original problem.

As frequency shift is a phenomenon that can be observed at speeds substantially below relativistic ones, I would find it immaterial to the stated concern.

 

[Venusian Broon]

Just to be clear, the physics and mathematics behind this are outside my level of expertise. I have simply treated this as a logic problem nd the dilation of distance seems to be a logical conclusion to maintain the speed of light as a constant.

Famously, I believe, Einstein reportedly developed his theory of relativity by mulling the thought experiment of "What would it be like to experience the perspective of a photon of light?" (I paraphrase)

And from his theory, it's pretty weird. Not only does it not experience any time, as we bunch of fermions observe it travelling at the speed of light, its length is effectively infinite as you've pointed out using the Lorentz factor. In 'practice' it has a length between where it was emitted to where it is 'stopped' by being absorbed (or observed, say), but it does not experience time. It's sort of a 'frozen instant' between two (to us) events

 

[Venusian Broon]

Famously, I believe, Einstein reportedly developed his theory of relativity by mulling the thought experiment of "What would it be like to experience the perspective of a photon of light?" (I paraphrase)

And from his theory, it's pretty weird. Not only does it not experience any time, as we bunch of fermions observe it travelling at the speed of light, its length is effectively infinite as you've pointed out using the Lorentz factor. In 'practice' it has a length between where it was emitted to where it is 'stopped' by being absorbed (or observed, say), but it does not experience time. It's sort of a 'frozen instant' between two (to us) events

Aarrgh noobie mistake. I put my hands up

'effectively infinite' is a bit misleading. It would be better to think of distance not being defined for a photon. (As we have a situation where we have something mathematically like one divided by zero. Which is undefined, not infinite.) The universe would sort of 'collapse to a no-dimensional point' for a photon, if my thinking is correct.

 

[CTRandall]

It would be better to think of distance not being defined for a photon. (As we have a situation where we have something mathematically like one divided by zero. Which is undefined, not infinite.) The universe would sort of 'collapse to a no-dimensional point' for a photon, if my thinking is correct.

Wheee! This is the kind of stuff I love! On the one hand, it points out just how much more we have to learn, as oddities like this suggest to me that we have an incomplete understanding of our universe. On the other hand, it illustrates the distance between maths and language. The maths may make sense but it is damned difficult to accurately translate it into English (or any other language), which means people like @Venusian Broon have to endlessly suffer through nincompoops like me using messy metaphors as the basis for all sorts of wacky ideas. Physicists must have been very naughty people in previous lives to be reincarnated into such a frustrating position.

 

[Venusian Broon]

Wheee! This is the kind of stuff I love! On the one hand, it points out just how much more we have to learn, as oddities like this suggest to me that we have an incomplete understanding of our universe. On the other hand, it illustrates the distance between maths and language. The maths may make sense but it is damned difficult to accurately translate it into English (or any other language), which means people like @Venusian Broon have to endlessly suffer through nincompoops like me using messy metaphors as the basis for all sorts of wacky ideas. Physicists must have been very naughty people in previous lives to be reincarnated into such a frustrating position.

Don't put yourself down! I always ask 'stupid' questions when it comes to areas of knowledge that I am a bit sketchy about and I always seem to forget some basics all the time. And there are loads of areas of knowledge I am very sketchy in .

Also I didn't really do relativity as a Physics graduate - Heriot-Watt was much more focused on experimental work, especially optics so their physics courses were more slanted to Quantum Mechanics and 'down-to-Earth' subjects rather than astrophysics, so it's been fun looking into it!

By coincidence I've been looking into Mathematics and Reality at the moment- a different sort of topic, but related. One feels, even with the cleverest of our thinkers that we really are still babes in the wood with really fundamental things about our perceived reality.

 

[CTRandall]

One feels, even with the cleverest of our thinkers that we really are still babes in the wood with really fundamental things about our perceived reality.

This is how I feel. Part of it is the disconnect between the fact that the math works but we have a hard time wrapping our heads around how it should be interpreted. The other part is that physics seems to be rubbing up against some of the foundations of our shared experience of the world: time, distance, velocity, for example.

I don't pretend to have the least notion of how to explain these things but thinking about them often inspires ideas for stories. (I've got one about the Copenhagen interpretation. It doesn't end well.)