# Time Dilation

1. May 31, 2009

### Sheneron

I asked a question similar to this a while ago but I couldn't get a straight answer; I think because of the way I worded the question so I am going to try again because I am really curious about the answer.

I have read that a distant observer will see an object slow down as it approaches a black hole event horizon and take an infinite time to reach it.

So does that mean that because the distant observer sees the objects clock ticking more slowly the object appears to physically slow down?

Then isn't the same true for an object accelerating (not necessarily near a black hole)? As an object accelerates to near the speed of light velocities will a distant observer see the object physically slow down and eventually almost be not moving?

It seems to me that either answer to the last question will create a contradiction.

2. May 31, 2009

### tiny-tim

acceleration does not cause time dilation

Hi Sheneron!
That's right.
What do you mean by "physically"?
Nope … gravity causes https://www.physicsforums.com/library.php?do=view_item&itemid=166" but acceleration does not

(velocity does, but that's independent of acceleration)

Last edited by a moderator: Apr 24, 2017
3. May 31, 2009

### Sheneron

Thanks for the response. Everytime I try to ask this question I screw up...

What I meant by 'physically slow down' is that not only is the objects clock ticking slower but it's speed is slower.

I meant to say "Then isn't the same true for an object accelerating to a high velocity."

Shouldn't an object at a high velocity have the same time dilation effects as an object accelerating to a high velocity near the event horizon of a black hole?

4. May 31, 2009

### qraal

Say the intrepid explorer venturing towards the black hole is sending back radio time-ticks to an observer far out of the hole's influence. The external observer will receive the time-ticks at an ever slower pace because of the increasing time-dilation as the explorer approaches the event horizon. Likewise an observer receiving time-ticks from an accelerating starship will receive the same time-signals at an ever slower rate as the starship approaches lightspeed. Both explorers are accelerating away from the observer, but the starship's acceleration is much lower, so the perceived time dilation takes longer to be apparent. Also the event horizon is crossed after a discrete time if that explorer is free-falling and not merely opposing the black hole's gravity, but the starship never crosses the speed of light 'event horizon'.

What about from the explorers' point of view? For the black hole explorer signals from the external observer are "blue shifted" - received at ever great frequency - as the explorer approaches the horizon. For the starship explorer signals from the observer are increasingly red-shifted if the starship is continually accelerated. The perceived passage of time, as counted by the time-signal from the observer left behind the starship, actually slows to a virtual halt. If the starship explorer never turns around and returns to the observer, the total perceived time elapsed, counted by clock-signals from home, approaches a fixed amount regardless of what the ship-board clock says. If the acceleration is 1 gee, then the total time - counted by clock-signals from the stationary observer - is just ~1.94 years, though the traveller might have accelerated for decades. Of course, back home, many millions of years will have passed.

5. May 31, 2009

### Sheneron

I still don't understand something, and it is my main question. Why at a black hole does the object stop moving because of time dilation, but for an object accelerating to near the speed of light velocities it doesn't slow down due to time dilation?

If something is moving at realllllyyyyy close to the speed of light, we see it moving really fast right? We don't see it moving slowly? But at a black hole something is moving really close to the speed of light and we see it stop moving completely at the event horizon.

6. May 31, 2009

### qraal

Hi Sheneron

An object keeps falling, taking a brief time to fall into a small black-hole in its moving reference frame, but the light that we see it by takes longer and longer to get back to us since it is 'red-shifted' to 'infinity' at the event horizon. In reality we'd see a final photon as the object crossed the line in a finite time, since light is quantised.

To fall to the centre of a Schwarzschild black-hole takes π.M/c seconds, where 'M' is (G*Mass/c².) For a Sun mass BH that happens in less than 1/64,000th of a second, but for the giant black-hole at the centre of M87 (3 billion solar masses) it'd take 13 hours. Such a super-massive black-hole journey might even be survivable, but just where that particular rabbit-hole lets you out is anyone's guess...

7. Jun 1, 2009

### Nabeshin

Last edited by a moderator: Apr 24, 2017
8. Jun 1, 2009

### qraal

Re: acceleration does not cause time dilation

Or basic physics. Acceleration is independent of velocity???

So they're not the first and second derivatives of position after all...

9. Jun 1, 2009

### granpa

if you are going to compare acceleration and gravity then you should probably know that a continuously accelerating observer will see a kind of black hole behind themselves. a region from which no light will ever reach them. that is what you should compare to the real black hole (assuming that they are real)

10. Jun 1, 2009

### tiny-tim

Re: acceleration does not cause time dilation

Hi Nabeshin!

I don't think the equivalence principle does show any https://www.physicsforums.com/library.php?do=view_item&itemid=166" for an accelerating frame, relative to a non-accelerating one.

(Though it does show time dilation within an accelerating frame.)

Imagine a very long lift, in whch we perform the famous http://en.wikipedia.org/wiki/Pound-Rebka_experiment" [Broken] …

(a) if the lift is stationary in a gravitational field, then identical clocks placed at the top and bottom of the lift will run at different rates, as seen by the loss in energy of a photon "climbing" from the bottom to the top of the lift, which causes a change in wavelength of the photon …

(b) and if the lift is accelerating in outer space, so as to produce the same acceleration of g, then again the wavelength of the photon changes, because a photon going from top to bottom meets the bottom when the lift is moving faster (as measured by a non-accelerating observer), and therefore is blue-shifted (and similarly is red-shifted at the top), and therefore again identical clocks placed at the top and bottom run at different rates.

But the same non-accelerating observer does not regard the clock-rate as dependent on the acceleration of the lift … the calculations in part (b) are based only on the velocity of the lift.

The clocks in the lift go slower (as measured by the non-accelerating observer) only because of their velocity, and that itself is enough to explain the time dilation along the lift.

Last edited by a moderator: May 4, 2017
11. Jun 1, 2009

### granpa

imagine a long line of stationary and synchonized clocks and a stationary observer. if the observer then accelerates to velocity v the clocks will appear to him to be out of synch. therefore during the acceleration the clocks at different distances from him appeared to him to run at different rates.

but what about clocks in his own accelerating frame?

edit:its the same unless you consider that his own ship is also contracting

Last edited: Jun 1, 2009
12. Jun 1, 2009

### Nabeshin

Re: acceleration does not cause time dilation

Okay, time dilation within the non-inertial reference frame is what I was initially thinking of. However, I'm still not convinced that acceleration plays no role.

Your situation a) makes perfect sense to me, but I'm having a hard time with b). I can accept that in the accelerating frame we observe relative shifts in wavelengths and conclude our clocks are out of synch. I think your next statement refers to the fact that the time dilation would be calculated by SR, not GR?

My confusion mainly lies in that during the discussion of b) we're talking about differences in rates among the two clocks in the accelerated frame, whereas after that you appear to be talking about differences between the two accelerating clocks and a clock attached to the non-accelerating observer?

Last edited by a moderator: May 4, 2017
13. Jun 1, 2009

### tiny-tim

Re: acceleration does not cause time dilation

Yes … we calculate in the non-accelerating frame, using SR: we prove that the two clocks go at different rates, and then we use the Equivalence Principle to deduce that the same happens in gravity.
Yes, clocks slowing in gravity means as viewed by a non-accelerating observer … so we compare a clock-in-gravity with a distant clock.

The equivalent would be comparing an accelerating clock with a distant clock, not comparing two accelerating clocks.