How can any speed be defined as a constant?

5,506

Solution 1

Speed of light is actually a pretty special case compared to how we typically think of speed (as far as I understand it).

Movement is always relative to some frame of reference. In the case of a single isolated object, it's hard to really think about how you could have any frame of reference without at least a second object to measure the speed relative to. With multiple objects, the relative velocity obviously depends on the movement of each object relative to each other.

Light is a special case because it has the same speed relative to any inertial reference frame. If I'm moving 3 km/s compared to Earth, for example, and someone else were moving 30,000 km/s compared to Earth, we would still both measure light moving at the speed of light relative to each of our reference frames. It's not exactly intuitive, but it's how we've found reality actually works.

It also leads to other weird consequences, like length contraction and time dilation.

Solution 2

My question is: If speed is not an entity in itself, but only dependent on other constant factors, how can the speed of anything (let alone light) be a constant? Am I completely missing something here?

The question you are really asking is which is the more fundamental, speed or distance? Think about the distances in space. How are we to measure them if we do not measure the time taken for something travelling at known speed? Think too about the structures of matter, how does a ruler maintain its size? It is because of the forces in bondings between atoms or molecules. Those forces are electromagnetic. The are transmitted by photons, in effect by particles of light. It is the speed of the forces (i.e. the speed of light) which create structure and give length to the ruler. Ultimately distance depends on speed, not speed on distance.

Either there is, or there is not, an absolute maximum speed in nature. If there were not, the laws of physics would be different from those we observe. So we know that there is a maximum speed. It happens that light travels at the maximum speed. Because distance depends on speed, all other speeds are fractions of the maximum speed. The speed of light is a constant because all speed are relative to the speed of light.

Solution 3

It is counter intuitive, this question or variants of it get asked a lot. Surely if you're travelling towards a beam of light it will appear to be travelling faster? The answer is it won't, every inertial observer measures the speed of light to be exactly $c$, regardless of their velocity. It is for this reason that the Galilean transformations break down and in their place we use the Lorentz transformations:

$$t'=\gamma\left(t-\frac{vx}{c}\right)\tag{1},$$ $$x'=\gamma(x-vt)\tag{2},$$ $$y'=y\tag{3},$$ $$z'=z\tag{4}.$$

It is also from this seemingly counter intuitive fact that length contraction and time dilation in special relativity appear.

Solution 4

how speed can be a constant

It's not, it depends on selected reference frame. The only exception is light speed in vacuum, which in any reference frame is $c$.

But what if the Earth itself now starts moving? Now the distance is still changing, but how the individual speeds be calculated?

In a pre-relativity times there was a Galilean speed addition rule :

$$ \mathbf {u} =\mathbf {v} +\mathbf {u'} $$

So if train goes at $100 \,\text{km/h}$ speed relative to ground, and you as passenger are walking inside a train wagons towards a driver with a $5\, \text{km/h}$ speed, then you may think that your speed relative to approaching crossroad is $100 + 5 = 105 \,\text{km/h} ?$

MAYBE.

In this particular case 105 is good approximation because your and train relative speeds is $\ll c$. But let's return back to your rocket-earth example.

Suppose that you want to return back to earth, so you reverse your rocket direction and start moving towards earth with $0.5c$ speed. Now, like you said some cosmic cataclysm has happened, near super-nova has exploded and explosion wave pushed earth towards your rocket also at $0.5c$ speed. So you may think that now your rocket speed towards earth will be $0.5c + 0.5c = 1c$ ?

NO

Simply because only light in vacuum and other massless particles can achieve light speed. Other objects with rest mass $> 0$ can neither reach $c$ nor exceed it. So to be able to correctly calculate your rocket speed towards earth you need to use special relativity speed addition formula, which is : $$ u={v+u' \over 1+(vu'/c^{2})} $$

This is also called a composition law for velocities. Now we plug your and earth relative velocities to CMB and get :

$$ \large{u={0.5c+0.5c \over 1+\left(\frac{0.5c \,\, 0.5c}{c^{2}}\right)}} = 0.8c $$

So your rocket moves towards accelerated earth only with $0.8$ of light speed. If you find it interesting, try to raise relative speeds to CMB of earth,rocket and see what happens. (Hint: Can you reach $c$ ?)

Now delete the Earth, and we have only a moving rocket in the entire universe. How can its speed be calculated? How do we even know it's still moving?

Indeed, if there are no external objects to compare with, it's hard to say a rocket is moving at all. However to remove all external reference frames would be impossible to do. At least you can measure rocket speed with respect to it's exhaust. The same as you see in a moving car like it leaves dirty fog behind. Or you can measure how cosmic microwave background radiation wavelength changes due to Doppler blue/red shift, which happens due to your rocket movement and etc.

Solution 5

If speed is not an entity in itself, but only dependent on other constant factors, how can the speed of anything (let alone light) be a constant? Am I completely missing something here?

What you are missing is that distance and time themselves are not constant. Both distance and time depend in part on the velocity of the observer.

  1. You are on Earth, and determine that the distance to the Sun is 93 million miles.
  2. You get on a rocket and start flying towards the Sun. You check again and find that the distance, not just between you and the Sun, but between Earth and the Sun is now only 90 million miles even though neither of them has moved towards the other.
  3. You turn on your radio and call your friend back on Earth. He says the Earth-Sun distance is still 93 million miles.
  4. You turn your rocket around and stop, now motionless between Earth and the Sun. You confirm that the Earth-Sun distance is 93 million miles.
  5. You turn the rocket back on to head home, and find that the Earth-Sun distance has somehow shrunk to 90 million miles again.
  6. You arrive at home and check the clock. You've been gone 30 minutes.
  7. You check your phone that you brought with you on the trip, which is still in airplane mode and hasn't synced yet, and it says you left only about 29 minutes ago.

The thing about the speed of light is that it's not actually light that's special. I've seen the speed of light referred to as the speed of causality, the speed of information, the universal speed limit, the cosmic speed limit, and probably a few more terms I haven't thought of right now.

The speed of light is the fastest that anything can move, and all things that have no mass will always travel at that speed. This speed is more fundamental than distance or time, and anything moving at that speed will always be measured as having that speed regardless of the measurer's movement.

This necessarily requires that people moving at different velocities will see the same interval as having different lengths, in both distance and time. This means that space and time contort in some strange and difficult to understand ways based on your movement, and Relativity is essentially an extended exercise in analyzing exactly what contortions are needed to produce an invariant speed. In any case, the effects of this for moving at any speed you've ever experienced are far too small to notice.

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Comments

  • half of a glazier
    half of a glazier over 3 years

    We know that the speed of light is a constant, and can therefore be used to calculate many other relative values, but I'm having difficulty understanding how speed can be a constant, seeing as it's dependent on other variables.

    For example, take a universe in which there is nothing other than Earth and the Sun. No other stars, galaxies, planets. In this example, when a rocket leaves Earth and heads towards the Sun, its speed is measurable, according to its varying distance from the Earth and the Sun.

    Now delete the Sun from the image. The rocket hasn't changed; it's still heading away from the Earth at the same speed. But what if the Earth itself now starts moving? Now the distance is still changing, but how the individual speeds be calculated?

    Now delete the Earth, and we have only a moving rocket in the entire universe. How can its speed be calculated? How do we even know it's still moving? Does the concept of 'speed' still exist?

    My question is: If speed is not an entity in itself, but only dependent on other constant factors, how can the speed of anything (let alone light) be a constant? Am I completely missing something here?

    Excuse the lack of scientific terms; I'm not a scientist; rather a software developer with an interest in relativity and quantum physics.

    Edit: The question is not "Is it possible to have a constant of speed?", in which case it would be possible to answer with, "Yes, and the proof is that there is a constant of speed, here's how to prove it...", which is what most of the answers seem to be doing.

    The question is rather "How can there be a constant of speed?" - emphasis on the 'constant' - in which case saying "Here's the proof that there is one" is not an answer. I know there is one, otherwise I wouldn't be asking the question...

    • tpg2114
      tpg2114 over 3 years
      I've deleted some comments that were attempting to answer the question... If you have an answer, please post it as one! Comments are to seek clarification or suggest improvements only. Thanks!
    • N. Virgo
      N. Virgo over 3 years
      This is quite clearly a duplicate of every "please explain relativity to me" question ever, of which there are very, very, very, very, very many. I'm voting to close as a duplicate as the first decent one that appeared in the linked questions.
    • tpg2114
      tpg2114 over 3 years
      Comments are not for extended discussion; this conversation has been moved to chat.
    • tpg2114
      tpg2114 over 3 years
      I've just deleted another round of answers in the comments. Please use these only to seek clarification or suggest improvements. Anything else should be an answer (if appropriate) or in the chat room if it isn't an answer.
    • Admin
      Admin over 3 years
      For your updated clarifications, see my simple answer. The only logical possibility seems to be a maximum relative speed.
  • half of a glazier
    half of a glazier over 3 years
    When you say "it's how we've found reality actually works", can you provide any links where I can read up on these examples?
  • JMac
    JMac over 3 years
    @Still_learning en.wikipedia.org/wiki/Tests_of_special_relativity Seems to have plenty of examples. To be honest, it's not really my area of specialty. There's quite a bit of history behind it.
  • BlueRaja - Danny Pflughoeft
    BlueRaja - Danny Pflughoeft over 3 years
  • supercat
    supercat over 3 years
    Do photons actually travel at the speed of causality, or at a value which is a very tiny bit slower than the speed of causality as a consequence of their small but non-zero mass?
  • Douglas
    Douglas over 3 years
    @supercat Photons have zero mass. You might be thinking of momentum.
  • Rexcirus
    Rexcirus over 3 years
    When you understand the "any inertial frame" part, you can appreciate how revolutionary special relativity is.
  • Post169
    Post169 over 3 years
    @JMac You might want to add a description or reference to define an inertial reference frame
  • Oscar Bravo
    Oscar Bravo over 3 years
    +1 for the sound advice of putting your phone in flight mode during interplanetary space-flight.
  • Ray
    Ray over 3 years
    @Still_learning Einstein's short book, "Relativity: The Special and General Theory". Part 1 essentially consists of him asking the same question you are: If all speed is relative to a reference frame, but the speed of light in a vacuum is constant, then what does that mean? And then working out the implications of that through a series of thought experiments and some basic algebra. (And then having learned what a constant speed of light implies, experiments were run to see if those things were true in reality. q.v. JMac's link)
  • Axel B
    Axel B over 3 years
    I don't really see how the electromagnetic interaction in the ruler being transmitted by photons adds anything to your argument