Photons & Time: t=0 What?

[spacecadet2563]

TL;DR

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As you move closer to the speed of light time begins to slow down for those looking from Earth. But time on the ship is normal for them. Go faster and slows down even more. Same thing. Time is normal. But I read when it reaches speed c the time on the ship goes to zero. I say wrong. Its still normal. Is that true?

 

[renormalize]

Is that true?

Yes, the time on the ship is still "normal" because relativity states that a massive ship must always move at less than the speed of light.

 

[Dale]

But I read when it reaches speed c the time on the ship goes to zero.

Be highly skeptical of any source that you read which discusses what happens on a ship that reaches $c$. It might be a great science fiction book, but it isn't a physics book.

 

[spacecadet2563]

But for light it goes or is at zero? Does the math say this? Why would clocks magically stop?
If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

 

[DaveC426913]

But for light it goes or is at zero?

No. Light does not experience time. There is no valid frame of reference for a photon.

This is a direct result of the postulates of Einsteinian Relativity.

In all frames of reference light is observed to move at c. If a photon could have a frame of reference, it would mean light would move at c in its frame of reference. Except, by definition, one is stationary in one's own frame of reference. This means that light would be both stationary and moving at c simultaneously - a direct contradiction.

If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

No. There is no "last" decimal.

99.999 999 99% c gives you a dilation factor of ~70,700.
99.999 999 999 9% c gives you a dilation factor of ~7,070,000.
99.999 999 999 999% c gives you a dilation factor of ~707,000,000.

If you were flying in your spaceship at 99.999 999 999 999% c ( 99.9⁽¹²⁾) you would see Earthlings almost frozen in time. A single heartbeat of an Earthling would appear to last more than two years to you.

And the factor just keeps getting bigger - and harder to achieve.

It is as hard to accerelate from 99.9⁽¹⁰⁾% to 99.9⁽¹²⁾%
as it is to accelerate from 99.9⁽⁸⁾ to 99.9⁽¹⁰⁾%.

 

[PeroK]

But for light it goes or is at zero? Does the math say this? Why would clocks magically stop?
If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

A clock can't travel at the speed of light. All motion between you and a clock is relative. If the clock is moving at 99% of the speed of light relative to you, then you are moving at 99% of the speed of light relative to the clock. Time dilation is relative and reciprocal. You measure the clock running slow and the clock measures your watch or heartbeat running slow. It's not physically possible for the relative speed to attain the speed of light. The mathematics cannot describe that scenario.

 

[A.T.]

But for light it goes or is at zero? Does the math say this? Why would clocks magically stop?
If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

Yes, according to the math, the clock rate approaches zero, when its speed approaches c. So if you take the limit, it is 0 at c. What that mathematical result means for light, is a matter of interpretation.

 

[PeroK]

Yes, according to the math, the clock rate approaches zero, when its speed approaches c. So if you take the limit, it is 0 at c. What that mathematical result means for light, is a matter of interpretation.

The limit is not part of the theory of special relativity.

 

[robphy]

For a ship (with nonzero rest mass), it cannot achieve "the speed of light" physically.
Although your Newtonian intuition suggests that
you can think in terms of "increments in velocity",
special-relativity implies that you should instead think in terms of "increments of rapidity" (which are additive, whereas velocities [like slopes] are not-additive).
Uniform impulses of 4-momentum would essentially move you along uniform increments of rapidity,
not uniform increments of velocity.

In terms of rapidity, "the speed of light" is infinitely far away.
(The area of the hyperbolic sector in a spacetime-diagram goes to infinity as you span the sector from
the 4-velocity "at rest in your initial frame" to
the 4-velocity "approaching the asymptotic-speed-of-light in your initial frame".)

 

[PeroK]

The limit is not part of the theory of special relativity.

For example, the Newtonian gravitational force is given by $F = \frac{Gm_1m_2}{r^2}$. In theory, two point particles can be arbitrarily close and the gravitational force arbitrarily large. But, the mathematics and the physical theory do not allow the limit of $r = 0$.

 

[spacecadet2563]

For a ship (with nonzero rest mass), it cannot achieve "the speed of light" physically.
Although your Newtonian intuition suggests that
you can think in terms of "increments in velocity",
special-relativity implies that you should instead think in terms of "increments of rapidity" (which are additive, whereas velocities [like slopes] are not-additive).
Uniform impulses of 4-momentum would essentially move you along uniform increments of rapidity,
not uniform increments of velocity.

In terms of rapidity, "the speed of light" is infinitely far away.
(The area of the hyperbolic sector in a spacetime-diagram goes to infinity as you span the sector from
the 4-velocity "at rest in your initial frame" to
the 4-velocity "approaching the asymptotic-speed-of-light in your initial frame".)

Thanks for all responses...

 

[Dale]

But for light it goes or is at zero? Does the math say this?

For light proper time (what clocks measure) is undefined.

What is mathematically defined for light is called an affine parameter. Proper time is an affine parameter for a massive object, but affine parameters for light (massless) and hypothetical faster than light particles are not proper times.

Why would clocks magically stop?

Because clocks have mass. Nothing with mass can go at $c$ or faster.

If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

It isn’t that the clocks stop when they reach that last decimal point. The clocks can never reach the last decimal point in the first place.

 

[Sagittarius A-Star]

But for light it goes or is at zero? Does the math say this? Why would clocks magically stop?
If that ship was 99.99999999 % light speed time would still be normal. But that last decimal point bang...the clocks stop.

For example: The distance from Earth to Alpha Centauri is 4.367 LY. If you travel with 99.99999999 % light speed (relative to Earth) to there, then the distance is length-contrated in your rest-frame by a factor of $1/70710.7$.

Calculation of gamma-factor:
https://www.wolframalpha.com/input?i2d=true&i=Divide[1,Sqrt[1-Power[\(40)0.9999999999\(41),2]]]

For the travel you would need approximately $0.000061758687$ years of your proper time.

Calculation:
https://www.wolframalpha.com/input?i2d=true&i=4.367+Divide[+1,0.9999999999+*+70710.7]

As others wrote, the spaceship cannot move with $100$ % of the speed of light.

 

[DaveC426913]

For the travel you would need approximately $0.000061758687$ years of your proper time.

That would be a commute of 30 minutes! Less than it takes me on a busy Monday.

 

[spacecadet2563]

For light proper time (what clocks measure) is undefined.

What is mathematically defined for light is called an affine parameter. Proper time is an affine parameter for a massive object, but affine parameters for light (massless) and hypothetical faster than light particles are not proper times.

Because clocks have mass. Nothing with mass can go at $c$ or faster.

It isn’t that the clocks stop when they reach that last decimal point. The clocks can never reach the last decimal point in the first place.

My point is not about clocks but time itself.

 

[robphy]

For a ship (with nonzero rest mass), it cannot achieve "the speed of light" physically.
Although your Newtonian intuition suggests that
you can think in terms of "increments in velocity",
special-relativity implies that you should instead think in terms of "increments of rapidity" (which are additive, whereas velocities [like slopes] are not-additive).

I should probably write the relevant formula involving hyperbolic-trigonometry.

$\beta=(v/c)=\tanh\theta$

so, $\frac{(v_1/c)+(v_2/c)}{1+(v_1/c)(v_2/c)}=\tanh(\theta_1+\theta_2)$

and

$\gamma=\frac{1}{\sqrt{1-(v/c)^2}}=\cosh\theta$

$\beta\gamma=\frac{(v/c)}{\sqrt{1-(v/c)^2}}=\sinh\theta$

and

$k=\sqrt{\frac{1+(v/c)}{1-(v/c)}}=\exp\theta$

(Of course, there's the familiar circular-trigonometry associated with Euclidean geometry.
Then, there is a Galilean-trigonometry due to I.M.Yaglom...
...all three as "trigonometry for affine Cayley-Klein geometry" but that's for another day.)

 

[Ibix]

My point is not about clocks but time itself.

If you can't even in principle describe a kind of clock that can travel at $c$ (and you can't), how can you say time is defined for something travelling at $c$? Relativity says you can't define it, and trying to apply the time dilation formula to say "time stops at $c$" turns out to involve a subtle self-contradiction.

 

[spacecadet2563]

If you can't even in principle describe a kind of clock that can travel at $c$ (and you can't), how can you say time is defined for something travelling at $c$? Relativity says you can't define it, and trying to apply the time dilation formula to say "time stops at $c$" turns out to involve a subtle self-contradiction.

I can measure what is going on from Earth...

 

[PeroK]

My point is not about clocks but time itself.

Time is what a clock measures. In this context, at least.

 

[DaveC426913]

I can measure what is going on from Earth...

The problem comes when you try to describe that scenario. The devil is in the details.

How would you know if time had stopped on a spaceship flying by at the speed of light (if it could), as opposed to just moving very slow?

 

[Ibix]

I can measure what is going on from Earth...

You can. That will show elapsed time, obviously since radar works. That has nothing to do with the "time that goes to zero", which is the (in the case of loght, undefined) proper time of the moving object.

 

[Sagittarius A-Star]

My point is not about clocks but time itself.

For example: If you send a light pulse from Earth to Alpha Centauri, then the spacetime-interval between the emition-event on Earth and the absorbtion-event on Alpha Centauri is zero.

But a spacetime-interval along a worldline is called "proper time" only for time-like worldlines, not for light-like worldlines.

 

[Dale]

My point is not about clocks but time itself.

No, it is about clocks. You repeatedly refer to velocity. "Time itself" doesn't have velocity, clocks do.

In physics we speak of two kinds of time: proper time and coordinate time. Proper time is the thing measured by a clock. Coordinate time is the coordinate labeled $t$ in a standard coordinate system. Your questions have been about proper time, so clocks are implied.

 

[Nugatory]

My point is not about clocks but time itself.

To quote Einstein: Time is what a clock measures.

At first glance this statement appears to be no more than a clever sound bite…. But it is actually a vital insight, maybe easier to appreciate if we compare it with the analogous “distance is what a ruler measures”.

If time is what a clock measures, then it should be clear that any discussion of time is at heart a discussion of the behavior of clocks (possibly hypothetical ones, as in “if we had a clock on a spaceship…”).