On the relativity of time and speed

[Student0027]

Speed can only be measured relative to some other object, like the speed of a tennis ball during a match at Wimbledon can only be measured relative to the ground, or a cloud, or the planet Mars.

On the other hand, time is relative. An object traveling at speeds approaching the speed of light in a vacuum (c) will experience time at a different rate than those objects traveling much slower. As an object's speed approaches c, time dilates for it. After a year passes for an object traveling near c, perhaps 100 years might have passed for objects traveling at much slower speeds.

But there is a contradiction here, isn't there? When you put the two statements together, you realize that everything is traveling at the speed of light in a vacuum, after all there is light traveling through space all the time. If we simply measure the speed of a light beam traveling away from Earth relative to our home planet, we realize that we are moving at the speed of light away from that light beam. If an object were to travel at near light speed along the same trajectory of that beam, then we would be traveling at near light speed relative to that object in the opposite direction. To an observer on that object, a year may have passed, while to us 100 years might have passed. And yet, to us a year may have passed, while to that observer on that object, 100 years might have passed. I'm just curious, am I missing something? Have there been any answers to this paradox?

 

[phinds]

There is no paradox. You are making the very common beginner's mistake of confusing time dilation, which is observed in other objects (never you) with differential aging. You, right now as you read this, are MASSIVELY time dilated according to a particle in the CERN accelerator and you are mildly time dilated according to a very fast asteroid passing by, and you are not time dilated at all according to the chair you are sitting in. BUT ... if you and another object travel through different space-time paths, you can join back up and find that different amounts of time have passed for the two of you. That's differential aging.

 

[Andrew Mason]

On the other hand, time is relative. An object traveling at speeds approaching the speed of light in a vacuum (c) will experience time at a different rate than those objects traveling much slower. As an object's speed approaches c, time dilates for it. After a year passes for an object traveling near c, perhaps 100 years might have passed for objects traveling at much slower speeds.

Not quite. The situation is symmetrical. Each observer measures the other observer's clocks to be running slow.

But there is a contradiction here, isn't there? When you put the two statements together, you realize that everything is traveling at the speed of light in a vacuum, after all there is light traveling through space all the time. If we simply measure the speed of a light beam traveling away from Earth relative to our home planet, we realize that we are moving at the speed of light away from that light beam. If an object were to travel at near light speed along the same trajectory of that beam, then we would be traveling at near light speed relative to that object in the opposite direction. To an observer on that object, a year may have passed, while to us 100 years might have passed. And yet, to us a year may have passed, while to that observer on that object, 100 years might have passed. I'm just curious, am I missing something? Have there been any answers to this paradox?

Photons (a stream of which constitutes a light beam) cannot define an inertial reference frame. A photon moves at c relative to all inertial reference frames.

As stated above, inertial observers measure the clocks of other inertial observers to be running slower than their own. It is symmetrical. No paradox.

AM

 

[rkolter]

Speed can only be measured relative to some other object, like the speed of a tennis ball during a match at Wimbledon can only be measured relative to the ground, or a cloud, or the planet Mars.

You mean Velocity - velocity is speed plus direction - you need some outside frame of reference to measure velocity. Speed is directionless - you do not need an outside frame of reference to measure speed, and in fact if you are measuring speed relative to an outside frame of reference, you are measuring velocity. This is important because you later talk about relating the speed of light to the Earth - and the speed of light in a vacuum is not relative. It will always, always be measured as c, regardless of the frame of reference. You cannot measure the speed of light to be zero relative to the Earth moving at the speed of light away from the laser beam. This seems counter-intuitive but the answer as others provided is that time, not the speed of light, is relative.

 

[Student0027]

Thank you all for your responses! I haven't studied physics since high school (and that was done about 10 years ago), so while I do not completely understand your responses, I do understand that there are logical explanations that I would need more study to understand. I feel like you've all given me a place to begin.